A second degree Newton method for an inverse scattering problem for a dielectric cylinder

Abstract

The inverse obstacle scattering problem we are interested is to reconstruct the image of an infinitely long homogeneous dielectric cylinder from the far field pattern for scattering of a time-harmonic E-polarized electromagnetic plane wave. We extend the approach suggested by Kress and Lee [18] that combines the ideas of Hettlich and Rundell [10] and Johansson and Sleeman [14] for the case of the inverse problem for a perfectly conducting scatterer to the case of penetrable scatterer. The inverse problem is depended on a system of non-linear boundary integral equations associated with a single layer approach to solve the direct scattering problem. We show the mathematical foundations of the method and illustrate its feasibility by numerical examples